Keypoint algorithms were developed to focus on small sets of informative image points rather than entire images. Keypoints are detected via convolutional filters with specific mathematical forms, guaranteeing invariance to input image translation [1]}, scaling [2]}, similarity [3]} and affine deformations [4]}. Keypoint methods remained the defacto standard for image-based learning until the development of programmable graphics processing units (GPUs), e.g. the Compute Unified Device Architecture (CUDA) development system, that could be used to train full image-based CNNs via massive parallelization of the backpropagation learning algorithm [5]}. This article focuses on the SIFT algorithm designed for keypoint extraction by David Lowe in 1999 [3]}. The backbone of the SIFT algorithm is the Gaussian scale-space [7]} generated via recursive Gaussian convolution filtering, it can be generated efficiently via separable and even uniform 1D filters [8]}. Advantages of the SIFT algorithm include the fact that keypoints are identified in a manner invariant to image resolution, object pose, or intensity variations, no training procedure or data are required, Gaussian and Gaussian derivative filters are rotationally symmetric and uniformly sampled and unbiased by the specific training data used. For these reasons, the SIFT keypoint algorithm and descriptor remains and efficient, competitive solution in contexts with few training examples, i.e. matching images of the same specific 3D objects [9]} or scenes [10]}. The functioning of the SIFT algorithm is analogous to aspects of visual processing within the mammalian vision system, including retinal center-surround processing in the lateral geniculate nucleus and oriented gradient operators organised into hypercolumns [11]}. The scale-space derived from Gaussian convolution \(I(x,y,z,\sigma )=I(x,y,z)*N(\sigma )=\)  representing the process of isotropic diffusion of particles (ex. Brownian motion ) or heat. The Laplacian-of-Gaussian \(\nabla ^2 I(x,y,z,\sigma )\)  is a scale-normalized operator analogous to the Laplacian operator forming the kinetic energy component of the Hamiltonian, e.g. as found in the Schrodinger equation.
